Dynamics and curl ratio of a curling stone

An attempt to develop a dynamic model for the motion of a curling stone is reported. Characteristic forms of the ice surface covered with many small pebbles and the narrow annular running band at the bottom of a stone lead to the increase in the force exerting on ice, resulting in the reduction of friction coefficient of ice and the production of ice fragments to increase the effective friction coefficient at the rear running band. In this paper, a numerical model is presented to compute the dynamic motion of a curling stone on the base of the evaporation–abrasion mechanism. The friction magnification factor, A, was introduced to evaluate the asymmetry that the friction coefficient of the rear running band is larger by a factor of A than that of the front. Numerical computations showed that curl distances and trajectories experienced in usual curling games were reproduced by magnitudes 5 ≤ A ≤ 20. Another physical quantity, curl ratio, C, was introduced to describe quantitatively the amount of curl of a stone moving with definite translational and angular velocities. C specifies the direction to which a stone moves at any instant. It increases with decreasing translational velocity and increasing angular velocity. In other words, a stone curls more at smaller speeds and higher turns.